VTMO 2013 — Grade 9 — semifinal Question 12

Question 12

$ABCD$ is cyclic and $AC \perp BD$ at $I$, with $IA = 3 \,\mathrm{cm} , IB = 4 \,\mathrm{cm} , ID = 6 \,\mathrm{cm}$. Find $CD$.

Question illustration

$8 \,\mathrm{cm}$
$7 \,\mathrm{cm}$
$12 \,\mathrm{cm}$
$10 \,\mathrm{cm}$
$18 \,\mathrm{cm}$